Mpofu scalped Tamim Iqbal, Mahmudullah and skipper Shakib al Hasan as Bangladesh were all out for 200 in 49 overs, having been set a modest target. Shakib and Mahmudullah steadied the innings with 54 for the seventh wicket before Mpofu struck again to dismiss Mahmudullah, caught by Chamu Chibhabha at long-on for 14.
Mpofu then got rid of Shakib, top-scorer with 63 from 65 balls, leaving Bangladesh on 195 for nine before a fourth run out finally sank them.
Earlier, left-arm spinner Abdur Razzak took four for 41 to help restrict Zimbabwe to 209 all out. Regis Chakabva, playing only his second one-dayer, top scored with 45. The second match is at the same venue on Friday.
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